Preference Aggregation Theory Without Acyclicity: The Core Without Majority Dissatisfaction

  title={Preference Aggregation Theory Without Acyclicity: The Core Without Majority Dissatisfaction},
  author={M. Kumabe and H. R. Mihara},
  journal={Games \& Political Behavior eJournal},
Acyclicity of individual preferences is a minimal assumption in social choice theory. We replace that assumption by the direct assumption that preferences have maximal elements on a fixed agenda. We show that the core of a simple game is nonempty for all profiles of such preferences if and only if the number of alternatives in the agenda is less than the Nakamura number of the game. The same is true if we replace the core by the core without majority dissatisfaction, obtained by deleting from… Expand

Topics from this paper

Characterizing the Borda ranking rule for a fixed population
A ranking rule (social welfare function) for a fixed population assigns a social preference to each profile of preferences. The rule satisfies "Positional Cancellation" if changes in the relativeExpand
The stability of decision making in committees: The one-core
We study the stability of decision making in committees. A policy proposal introduced by a committee member is either adopted or abandoned in favor of a new proposal after deliberations. If aExpand
Computability of Simple Games: A Complete Investigation of the Sixty-Four Possibilities
If a type contains an infinite game, then it contains both computable ones and noncomputable ones, which strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms. Expand


The stability set of voting games: Classification and genericity results
In 1980 Rubinstein introduced a new solution concept for voting games called the stability set which incorporates the idea that before entering into a possibly winning coalition with respect to someExpand
A note on the non-emptiness of the stability set when individual preferences are weak orders
Abstract It is well known from the Nakamura's theorem [Nakamura, K., 1979. The vetoers of a simple game with ordinal preferences, International Journal of Game Theory 8, 55–61.] that the core of aExpand
A systematic approach to the construction of non-empty choice sets
  • John Duggan
  • Mathematics, Computer Science
  • Soc. Choice Welf.
  • 2007
This paper proposes to delete particular instances of strict preferences until the resulting relation satisfies one of a number of known regularity properties (transitivity, acyclicity, or negative transitivity), and to unify the choices generated by different orders of deletion. Expand
Acyclic social choice from finite sets
This paper characterizes acyclic preference aggregation rules under various combinations of monotonicity, neutrality, decisiveness, and anonymity, in the spirit of Nakamura's (1979) Theorem on theExpand
Social choice and electoral competition in the general spatial model
The properties of social preferences generated by simple games are investigated; results on generic emptiness of the core are extended; the general nonemptiness of the uncovered and undominated sets is proved; and the upper hemicontinuity of these correspondences is proved. Expand
The vetoers in a simple game with ordinal preferences
We consider a core of a simple game with ordinal preferences on a set of alternative outcomes Ω. When a player's strict preference relation takes any logically possible form of acyclic binaryExpand
Coalitionally strategyproof functions depend only on the most-preferred alternatives
Abstract. In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy “tops only.” That is, they depend only on which alternativeExpand
Voting games and acyclic collective choice rules
Abstract The subject of this paper is the representation of collective choice rules by voting games and the acyclicity of these rules. A collective choice rule is a function that associates aExpand
Revealed Conflicting Preferences
We model a DM as a collection of utility functions (selves, rationales) and an aggregation rule (a theory of how selves are activated by choice sets). The DM’s choice function is rationalized by aExpand
The Nakamura numbers for computable simple games
It is found that a computable game has a finite Nakamura number greater than three only if it is proper, nonstrong, and nonweak, regardless of whether it is monotonic or whether it has a infinite carrier. Expand